Neither the Reformation nor the Counter-reformation are noted for their tolerance of differnt opinions on religion or science or politics. If there was any relief at all, it came in the political divisions of Europe, divisions that effectively meant that there were always some places that were more liberal than others.

The Church, and especially the Jesuits, did support a hgih level of learning. It may have been 'classical' in orientation, but it did serve to raise the intellectual level of Europeans.

On Bruno and the Inquisition

Bruno, as did many of his contemporaries, actively engaged / espoused a wide variety to new theories, not only that of Copernicus but also those of Nicholas of Cusa (plural worlds, etc.) and especially elements of magic and of the Arianist (denies the divinity of Christ) heresy. Most importantly he was a very public and very controversial figure; unlike Galileo, he refused to abjure his beliefs.

Specifically:

Holding opinions contrary to the Catholic Faith and speaking
against it and its ministers.

Holding erroneous opinions about the Trinity, about Christ's
divinity and Incarnation.

Holding erroneous opinions about Christ.

Holding erroneous opinions about Transubstantiation and Mass.

Denying the Virginity of Mary

Claiming the existence of a plurality of worlds and their eternity.

Believing in metempsychosis and in the transmigration of the
human soul; the same soul inhabits in succession the bodies of different beings, both humans and animals.

Dealing in magic and divination; alchemy .

But note the following:
items 2, 3, 4 and 5 are characteristics of Arianism and contrary to the Nicaean / Orthodox creed. They make him a heretic.
item 6 and 7 are atomistic in character, and deny the special role of humans in creation
item 7: there is lots of evidence for this, but many others did it as well including Newton

Arrested by the inquisition he was tried and executed. To be 'burnt at the stake' ['purification by fire'] was a well established medieval practice for dealing with witchcraft and heresy, as well as for wives who murdered their husbands.

Note that other prominent scholars of the period dabbled in many of the same things, tho not quite as conspicuously as did Bruno. His espousal of heresy and of the Copernican model seemed to be related, eventually ensuring that Copernicus' thesis would end on the Index of Forbidden Books in 1616.

Protestant Europe was no better:

Servetus...a notable pioneer in the field of physiology; charge him with destroying the very foundations of Christianity by various heresies as to the Trinity, the person of Christ, the immortality of the soul, and infant baptism; and finally led up to the climax by charging that he had defamed Calvin. In Geneva, Switzerland, there was dedicated in 1912 a monument bearing the following inscription: "In memory of Michael Servetus--victim of religious intolerance of his time, and burned for his convictions at Champel, on September 27, 1553. Erected by the followers of John Calvin, three hundred and fifty years later, as expiation for that act, and to repudiate all coercion in matters of faith."

Walther Kohler "In Luther's case it is impossible to speak of liberty of conscience or religious freedom . . . The death-penalty for heresy rested on the highest Lutheran authority . . . The views of the other reformers on the persecution and bringing to justice of heretics were merely the outgrowth of Luther's plan; they contributed nothing fresh.
(Reformation und Ketzerprozess, 29 ff.). Luther: "I am on the heels of the Sacramentaries and the Anabaptists; . . . I shall challenge them to fight; and I shall trample them all underfoot."

Will Durant
"Calvin was as thorough as any pope in rejecting individualism of belief; this greatest legislator of Protestantism completely repudiated that principle of private judgment with which the new religion had begun. He had seen the fragmentation of the Reformation into a hundred sects, and foresaw more; in Geneva he would have none of them."

The popular perception is that Galileo

was hounded by the Church authorities because of his unorthodox views of the cosmos including the challenge to the Aristotelian/Ptolomaic model.

was fortunate to excape the fate of Bruno (1548 - 1600), who, it is alleged was burned at the stake for advocating the Copernican model (and also gave his name to a major crater on the moon)..

But that is part of the story.

Until 1616, however the Jesuits were actively and productively engaged in astronomy and made extensive use of the telescope and like Galileo, also observed the planets of Jupiter. Jesuit centers of learning

Christopher Clavius, foremost Jesuit defender of the Ptolemaic system, writing in 1612 and after having a chance to use the telescope .

I do not want to hide from the reader that not long ago a certain instrument was brought from Belgium. It has the form of a long tube in the bases of which are set two glasses, or rather lenses, by which objects far away from us appear very much closer . . . than the things themselves are. This instrument shows many more stars in the firmament than can be seen in any way without it, especially in the Pleiades, around the nebulas of Cancer and Orion, in the Milky Way, and other places . . . and when the Moon is a crescent or half full, it appears so remarkably fractured and rough that I cannot marvel enough that there is such unevenness in the lunar body. Consult the reliable little book by Galileo Galilei, printed at Venice in 1610 and called Sidereus Nuncius, which describes various observations of the stars first made by him.

Far from the least important of the things seen with this instrument is that Venus receives its light from the Sun as does the Moon, so that sometimes it appears to be more like a crescent, sometimes less, according to its distance from the Sun. At Rome I have observed this, in the presence of others, more than once.[Note: this is complex to explain, but the geocentric model predicts a different pattern] Saturn has joined to it two smaller stars, one on the east, the other on the west.[1] Finally Jupiter has four roving stars, which vary their places in a remarkable way both among themselves and with respect to Jupiter--as Galileo Galilei carefully and accurately describes. Since things are thus, astronomers ought to consider how the celestial orbs may be arranged in order to save these phenomena.[2]

Note: Among the solutions, that the sun moves around the earth and the other planets around the sun, but that posed a major problem for it ultimately meant there was more than one center of rotation: That is, and this is the critical point for refuting the Aristotelian / Ptolemaic model: The satellites of Jupiter had now shown that no matter what arrangement one preferred, there was more than one center of rotation.